Skip to main content

Теория: 03 Метод рационализации (только задачи)

Задание

Таблица соотвествий неравенств в области определения

\(\displaystyle \sqrt{\color{green}{f(x)}}-\sqrt{\color{blue}{g(x)}} \vee 0\) \(\displaystyle \color{green}{f(x)}-\color{blue}{g(x)} \vee 0\)
\(\displaystyle |\color{green}{f(x)}|-|\color{blue}{g(x)}|\ \vee 0\) \(\displaystyle (\color{green}{f(x)}-\color{blue}{g(x)})(\color{green}{f(x)}+\color{blue}{g(x)}) \vee 0\)
\(\displaystyle \log_{\color{red}{h(x)}}(\color{green}{f(x)}) \vee 0\) \(\displaystyle (\color{red}{h(x)}-1)(\color{green}{f(x)}-1) \vee 0\)
\(\displaystyle \log_{\color{red}{h(x)}}(\color{green}{f(x)})-1 \vee 0\) \(\displaystyle (\color{red}{h(x)}-1)(\color{green}{f(x)}-\color{red}{h(x)}) \vee 0\)
\(\displaystyle \log_{\color{red}{h(x)}}(\color{green}{f(x)})-a \vee 0\) \(\displaystyle (\color{red}{h(x)}-1)(\color{green}{f(x)}-\color{red}{h(x)}^{a}) \vee 0\)
\(\displaystyle \log_{\color{red}{h(x)}}(\color{green}{f(x)})-\log_{\color{red}{h(x)}}(\color{blue}{g(x)}) \vee 0\) \(\displaystyle (\color{red}{h(x)}-1)(\color{green}{f(x)}-\color{blue}{g(x)}) \vee 0\)
\(\displaystyle \log_{\color{red}{h(x)}}(\color{green}{f(x)})-\log_{\color{blue}{g(x)}}(\color{green}{f(x)}) \vee 0\) \(\displaystyle (\color{red}{h(x)}-1)(\color{blue}{g(x)}-1)(\color{green}{f(x)}-1) (\color{blue}{g(x)}-\color{red}{h(x)})\vee 0\)
\(\displaystyle \color{red}{h(x)}^{\color{green}{f(x)}}-1 \vee 0\) \(\displaystyle (\color{red}{h(x)}-1)\color{green}{f(x)} \vee 0\)
\(\displaystyle \color{red}{h(x)}^{\color{green}{f(x)}}-\color{red}{h(x)}^{\color{blue}{g(x)}} \vee 0\) \(\displaystyle (\color{red}{h(x)}-1)(\color{green}{f(x)}-\color{blue}{g(x)}) \vee 0\)
\(\displaystyle \color{green}{f(x)}^{p(x)}-\color{blue}{g(x)}^{p(x)} \vee 0\) \(\displaystyle p(x) (\color{green}{f(x)}-\color{blue}{g(x)}) \vee 0\)

 

Решение